The temperature of $O_2$ gas at which its $r.m.s.$ speed is equal to the most probable speed of $H_2$ gas at $300 \ K$ is ............... $K$.

Select the correct order of molecular speeds for a gas.

At what temperature $(^o C)$ will the $rms$ speed of $CO_2$ be equal to the $rms$ speed of $CO$ at $STP$?

The r.m.s. velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x \ cm \ s^{-1}$. At what temperature (in kelvin), the r.m.s. velocity of nitrous oxide would be $4 x \ cm \ s^{-1}$ (in $T$)? (Atomic weights of $C, N$ and $O$ are respectively $12, 14$ and $16$)

The ratio between the most probable speed of $N_2$ at $400 \ K$ and $CO$ at $800 \ K$ is (molar mass of $N_2 = 28 \ g \ mol^{-1}$, molar mass of $CO = 28 \ g \ mol^{-1}$)

The ratio of the $rms$ speed of $H_2$ at $50 \ K$ to the $rms$ speed of $O_2$ at $800 \ K$ is ......